两道数学题
1、因式分解:(x+y)^3(x-y)-(x+y)(x-y)^3
2、如果a,b满足a^2b^2+a^2+b^2+10ab+16=0,求a^2+b^2的值
参考答案:1、(x+y)^3(x-y)-(x+y)(x-y)^3
=(x+y)(x-y)[(x+y)^2-(x-y)^2]
=(x+y)(x-y)[(x+y+x-y)(x+y-x+y)]
=4xy(x+y)(x-y)
2、如果a,b满足a^2b^2+a^2+b^2+10ab+16=0,求a^2+b^2的值
a^2b^2+a^2+b^2+10ab+16=0,
(ab+8)^2+(a+b)^2=0
所以,ab=-8,a+b=0
a^2+b^2=(a+b)^-2ab=16